We characterize the strength, in terms of Weihrauch degrees, of certain problems related to Ramsey-like theorems concerning colourings of the rationals and of the natural numbers. The theorems we are chiefly interested in assert the existence of almost-homogeneous sets for colourings of pairs of rationals respectively natural numbers satisfying properties determined by some additional algebraic structure on the set of colours. In the context of reverse mathematics, most of the principles we study are equivalent to $\Sigma^0_2$-induction over $\mathrm{RCA}_0$. The associated problems in the Weihrauch lattice are related to $\mathrm{TC}_\mathbb{N}^*$, $(\mathrm{LPO}')^*$ or their product, depending on their precise formalizations.

翻译：我们以Weihrauch度数为工具，刻画了与有理数和自然数着色相关的若干拉姆齐型定理对应问题的强度。我们主要关注的定理断言：对于满足由颜色集合上附加代数结构所确定性质的有理数对或自然数对着色，存在几乎齐次集。在逆数学语境下，我们研究的多数原理等价于$\mathrm{RCA}_0$上的$\Sigma^0_2$归纳法。Weihrauch格中的相关问题与$\mathrm{TC}_\mathbb{N}^*$、$(\mathrm{LPO}')^*$或其乘积相关联，具体取决于其精确形式化表述。